BINARY SUBFIELD CODES OF CODES OVER A CERTAIN CHAIN RING

In this article, we consider linear codes over the chain ring F-2[x]/< x(s)> with s >= 2 that are obtained using a construction referred to as the D-C-construction, where D is a set generated with the help of certain simplicial complexes. The main result is the utilization of the trace map tau:F-2[x]/< x(s)>-> F-2 given by a(0)+a(1)u+a(2)u(2)+center dot center dot center dot+a(s-1)u(s-1)bar right arrowa(0)+a(1)+center dot center dot center dot+a(s-1) to study binary subfield codes of CD-codes. These binary subfield codes are l-weight codes where l=1,2, or 4, and most of them are distance-optimal codes. Moreover, these binary codes are self-orthogonal and minimal under certain conditions. We present many new distance-optimal binary linear codes.